5d6 Dice Probability — Full Distribution and Odds
Yahtzee and fireball territory: 7,776 outcomes, and five of a kind is one of them. The sum runs from 5 to 30, the average is 17.5, and the most likely total is 17. Below is every sum with its exact number of ways, its probability, the cumulative odds and the "at least" thresholds worth memorising.
Every possible sum
| Sum | Ways | Exactly | At most | At least | Odds of exactly |
|---|---|---|---|---|---|
| 5 | 1 | 0.013% | 0.013% | 100.0% | 1 in 7776 |
| 6 | 5 | 0.064% | 0.077% | 100.0% | 1 in 1555 |
| 7 | 15 | 0.193% | 0.270% | 99.9% | 1 in 518 |
| 8 | 35 | 0.450% | 0.720% | 99.7% | 1 in 222 |
| 9 | 70 | 0.900% | 1.62% | 99.3% | 1 in 111 |
| 10 | 126 | 1.62% | 3.24% | 98.4% | 1 in 61.7 |
| 11 | 205 | 2.64% | 5.88% | 96.8% | 1 in 37.9 |
| 12 | 305 | 3.92% | 9.80% | 94.1% | 1 in 25.5 |
| 13 | 420 | 5.40% | 15.2% | 90.2% | 1 in 18.5 |
| 14 | 540 | 6.94% | 22.1% | 84.8% | 1 in 14.4 |
| 15 | 651 | 8.37% | 30.5% | 77.9% | 1 in 11.9 |
| 16 | 735 | 9.45% | 40.0% | 69.5% | 1 in 10.6 |
| 17 | 780 | 10.0% | 50.0% | 60.0% | 1 in 9.97 |
| 18 | 780 | 10.0% | 60.0% | 50.0% | 1 in 9.97 |
| 19 | 735 | 9.45% | 69.5% | 40.0% | 1 in 10.6 |
| 20 | 651 | 8.37% | 77.9% | 30.5% | 1 in 11.9 |
| 21 | 540 | 6.94% | 84.8% | 22.1% | 1 in 14.4 |
| 22 | 420 | 5.40% | 90.2% | 15.2% | 1 in 18.5 |
| 23 | 305 | 3.92% | 94.1% | 9.80% | 1 in 25.5 |
| 24 | 205 | 2.64% | 96.8% | 5.88% | 1 in 37.9 |
| 25 | 126 | 1.62% | 98.4% | 3.24% | 1 in 61.7 |
| 26 | 70 | 0.900% | 99.3% | 1.62% | 1 in 111 |
| 27 | 35 | 0.450% | 99.7% | 0.720% | 1 in 222 |
| 28 | 15 | 0.193% | 99.9% | 0.270% | 1 in 518 |
| 29 | 5 | 0.064% | 100.0% | 0.077% | 1 in 1555 |
| 30 | 1 | 0.013% | 100.0% | 0.013% | 1 in 7776 |
Rolling a target or higher
This is the form most checks actually use — "did I beat 12?" rather than "did I roll exactly 12".
| Target | Chance of meeting it | Odds |
|---|---|---|
| ≥ 14 | 84.8% | 1 in 1.18 |
| ≥ 16 | 69.5% | 1 in 1.44 |
| ≥ 18 | 50.0% | 1 in 2 |
| ≥ 21 | 22.1% | 1 in 4.52 |
| ≥ 23 | 9.80% | 1 in 10.2 |
Reading the shape
Each die is uniform, but the sum is not. 5d6 has 7,776 ordered outcomes spread over 26 totals, and the counts rise toward the middle because a middle total can be assembled from more orderings. The curve is symmetric around 17.5 — for every way to roll 16.5 there is a mirrored way to roll 18.5 — which is why the standard deviation of 3.82 describes the spread on both sides equally.
Compare that with a single die: 1d6 is a flat line at 16.7% per face. Adding dice does not widen the range proportionally — it makes extreme results rarer. That is the whole reason systems that want predictable outcomes roll pools, and systems that want drama roll one big die.
Frequently asked
What is the average roll of 5d6?
17.5. The formula is dice × (faces + 1) / 2 — 5 × (6 + 1) / 2 — which works for any fair die. The standard deviation is 3.82, so most rolls land between 13 and 22.
What is the most likely total on 5d6?
17 and 18, at 10.0% — 780 of the 7,776 equally likely outcomes. The extremes (5 and 30) take 1 way each, or 0.013%.
How many possible outcomes does 5d6 have?
7,776 ordered outcomes — 65 — collapsing into 26 possible sums from 5 to 30. The counts here are exact integers from a convolution, not a normal approximation, so the tails are right: a normal curve would misstate the odds of the extreme rolls.
Why is the middle so much more likely than the ends?
Because sums have more ways to happen than faces do. There is exactly one way to roll all ones, but a middle total can be assembled from many orderings, and each ordering is a distinct outcome. That is why 5d6 has a plateau at 17 and 18 and why adding dice makes the distribution tighter rather than wider.